1. 6-2 properties of parallelograms
Chapter 6
6-2 properties of parallelograms

2. Objectives
Prove and apply properties of parallelograms. Use properties of parallelograms to solve problems.

3. Parallelograms
Any polygon with four sides is a quadrilateral. However, some quadrilaterals have special properties. These special quadrilaterals are given their own names.

4. Parallelograms
A quadrilateral with two pairs of parallel sides is a parallelogram. To write the name of a parallelogram, you use the symbol

5. Properties of parallelograms

6. Properties of parallograms

7. Example#1 Properties of parallelogram
In CDEF, DE = 74 mm,
DG = 31 mm, and m FCD = 42°. Find CF.
CF = DE
CF = 74 mm

8. Example#2
In CDEF, DE = 74 mm,
DG = 31 mm, and mFCD = 42°. Find mEFC.
mEFC + mFCD = 180°
mEFC + 42 = 180
mEFC = 138°

9. Example#3 In CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°. Find DF.
DF = 2DG
DF = 2(31)
DF = 62

10. Example 2A: Using Properties of Parallelograms to Find Measures
WXYZ is a parallelogram. Find YZ.
YZ = 8a – 4 = 8(7) – 4 = 52
YZ = XW
8a – 4 = 6a + 10
2a = 14
a = 7

11. Example WXYZ is a parallelogram. Find mZ . mZ + mW = 180°
(9b + 2) + (18b – 11) = 180
27b – 9 = 180
27b = 189
b = 7
mZ = (9b + 2)° = [9(7) + 2]° = 65°

12. Example 3: Parallelograms in the Coordinate Plane
Three vertices of JKLM are J(3, –8), K(–2, 2), and L(2, 6). Find the coordinates of vertex M.
Since JKLM is a parallelogram, both pairs of opposite sides must be parallel.

13. solution
Step 1 Graph the given points. J K L

14. solution Step 2 Find the slope of by counting the units from K to L.
The rise from 2 to 6 is 4.
The run of –2 to 2 is 4.
Step 3 Start at J and count the
same number of units.
A rise of 4 from –8 is –4.
A run of 4 from 3 is 7. Label (7, –4) as vertex M.

15. solution J K L M
The coordinates of vertex M are (7, –4).

16. Example 4A: Using Properties of Parallelograms in a Proof
Write a two-column proof.
Given: ABCD is a parallelogram.
Prove: ∆AEB  ∆CED

17. Continue Proof: Statements Reasons 3.  diags. bisect each other
1. ABCD is a parallelogram
1. Given
 opp. sides 
4. SSS Steps 2, 3

18. Example Write a two-column proof.
Given: GHJN and JKLM are parallelograms. H and M are collinear. N and K are collinear.
Prove: H M

19. solution Statements Reasons 1. GHJN and JKLM are parallelograms.
1. Given
2. H and HJN are supp.
M and MJK are supp.
 cons. s supp.
3. HJN  MJK
3. Vert. s Thm.
4. H  M
4.  Supps. Thm.

20. Example Write a two-column proof.
Given: GHJN and JKLM are parallelograms.
H and M are collinear. N and K are collinear.

21. solution Statements Reasons 1. RSTU is a parallelogram. 1. Given
2. N and HJN are supp.
K and MJK are supp.
 cons. s supp.
3. HJN  MJK
3. Vert. s Thm.
4. N  K
4.  Supps. Thm.

22. Student guided Practice
Do even problems from 2-14 in your book page 407

23. Homework
Do even problems in your book page 407

24. Closure
Today we learned about properties of parallelograms

25. Have a great day